Method for determining and implementing electrical damping coefficients

ABSTRACT

In one implementation, a method for operating a plurality of MEMS devices including applying a magnitude of a selected actuation signal equal to a first substantially constant magnitude to an actuator to cause a movable structure to begin to accelerate from a first position to impact a motion stop at a second position. The method also includes decreasing the magnitude of the selected actuation signal in a first manner. The method further includes varying at least one of a start time and a duration of the decreasing magnitude of the selected actuation signal and observing a settling time of the movable structure in response to the step of varying. In some implementations, the method includes ascertaining a range of values for the start times and the corresponding durations for each of the plurality of MEMS devices that are capable of providing settling times of the movable structure in conformance with a predetermined specification based on the steps of varying and observing. Such an implementation can include using the ascertained range of values for each device and the selected actuation signal for determining an operating start time and a corresponding operating duration to construct an operating actuation signal capable of providing a settling time for all devices in conformance with the predetermined specification. The method also can include controlling a signal source with a programmed processor to selectively apply the operating actuation signal to the plurality of MEMS devices.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of copending U.S. patentapplication Ser. No. 09/783,730 filed Feb. 13, 2001, by Kruglick, etal., entitled METHOD AND APPARATUS FOR ELECTRONIC DAMPING OF COMPLEXDYNAMIC SYSTEMS, herein incorporated by reference in its entirety. Thisapplication is also related to U.S. patent application Ser. No.09/896,022, by Kruglick, entitled ELECTRONIC DAMPING OF MEMS DEVICESUSING A LOOK-UP TABLE, filed herewith, herein incorporated by referencein its entirety.

BACKGROUND

Optical switching plays an important role in telecommunication networks,optical instrumentation, and optical signal processing systems. Opticalswitches can be used to turn the light output of an optical fiber on oroff with respect to an output fiber, or, alternatively, to redirect thelight to various different fibers, all under electronic control. Opticalswitches that provide switchable cross connects between an array ofinput fibers and an array of output fibers are often referred to as“optical cross-connects.” Optical cross-connects are a fundamentalbuilding block in the development of an all-optical communicationsnetwork.

There are many different types of optical switches. One general class ofoptical switches may be referred to as “bulk optomechanical switches” orsimply “optomechanical switches.” Such switches employ physical motionof one, or more, optical elements to perform optical switching. Anoptomechanical switch can be implemented either in a free-space approachor in a waveguide (e.g., optical fiber) approach. The free-spaceapproach is more scalable compared to the waveguide approach.

In optomechanical switches employing the free space approach, opticalsignals are switched between different fibers by a number of differentmethods. Typically, these methods utilize selective reflection of theoptical signal off of a reflective material, such as a mirror, into afiber. The optical signal passes through free space from an input fiberto reach the mirror, and after reflection, passes through free space toan output fiber. The optical signals are typically collimated in orderto minimize coupling loss of the optical signal between an input andoutput fiber.

Micro-Electro-Mechanical Systems or MEMS are electrical-mechanicalstructures typically sized on a millimeter scale or smaller. Thesestructures are used in a wide variety of applications including forexample, sensing, electrical and optical switching, and micron scale (orsmaller) machinery such as robotics and motors. MEMS structures canutilize both the mechanical and electrical attributes of material toachieve desired results. Because of their small size, MEMS devices maybe fabricated utilizing semiconductor processing methods and othermicrofabrication techniques such as thin film processing andphotolithography. Once fabricated, the MEMS structures are assembled toform MEMS devices.

MEMS structures have been shown to offer many advantages for buildingoptomechanical switches. Namely, the use of MEMS structures cansignificantly reduce the size, weight and cost of optomechanicalswitches. The switching time can also be reduced because of the lowermass of the smaller optomechanical switches.

Movable MEMS structures are capable of oscillating uncontrollably ifthey are not damped. Such oscillation is due to MEMS structure designand/or fabrication. For example, very low friction in the hinges of MEMSstructures allows them to move easily and repeatedly bounce off ofstationary objects such as motion stops. Known methods for damping MEMSstructures do not provide quick and efficient damping for all types ofstructures. Thus, there is a need for a method and/or apparatus thatprovides quick and efficient damping of MEMS structures.

SUMMARY

In one implementation, a method for operating a plurality of MEMSdevices including applying a magnitude of a selected actuation signalequal to a first substantially constant magnitude to an actuator tocause a movable structure to begin to accelerate from a first positionto impact a motion stop at a second position. The method also includesdecreasing the magnitude of the selected actuation signal in a firstmanner. The method further includes varying at least one of a start timeand a duration of the decreasing magnitude of the selected actuationsignal and observing a settling time of the movable structure inresponse to the step of varying. In some implementations, the methodincludes ascertaining a range of values for the start times and thecorresponding durations for each of the plurality of MEMS devices thatare capable of providing settling times of the movable structure inconformance with a predetermined specification based on the steps ofvarying and observing. Such an implementation can further include usingthe ascertained range of values for each of the plurality of MEMSdevices and the selected actuation signal for determining an operatingstart time and a corresponding operating duration to construct anoperating actuation signal capable of providing a settling time for eachof the plurality of MEMS devices in conformance with the predeterminedspecification. In certain implementations, the method also can includecontrolling a signal source with a programmed processor to selectivelyapply the operating actuation signal to the plurality of MEMS devices.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a top view illustrating a two-dimensional optical switchhaving MEMS switching cells.

FIG. 2 is a simplified perspective view illustrating one of the MEMSswitching cells shown in FIG. 1 in the transmission position.

FIG. 3 is a simplified perspective view illustrating the MEMS switchingcell shown in FIG. 2 in the reflection position.

FIG. 4 is a plot illustrating an actuation signal and resulting outputsignal when the actuation signal is applied to the MEMS switching cellshown in FIG. 2.

FIG. 5 is a simplified perspective view illustrating the actuator plateof the MEMS switching cell shown in FIG. 2 bouncing off of the motionstop.

FIG. 6 is a plot illustrating an actuation signal in accordance with anembodiment of the present invention and the resulting output signal whenthe actuation signal is applied to the MEMS switching cell shown in FIG.2.

FIG. 7 is a plot further illustrating the actuation signal shown in FIG.6.

FIG. 8A is a representative plot illustrating the torque and velocitythat result from the actuation signal shown in FIG. 4.

FIG. 8B is a representative plot illustrating the torque and velocitythat result from the actuation signal shown in FIG. 6.

FIGS. 9A, 9B, 9C, 9D, 9E and 9F are plots illustrating actuation signalsin accordance with alternative embodiments of the present invention.

FIG. 10 is a plot illustrating an actuation signal in accordance withanother embodiment of the present invention and the resulting outputsignal when the actuation signal is applied to the MEMS switching cellshown in FIG. 2.

FIG. 11 is a block diagram illustrating an exemplary system forgenerating the actuation signal shown in FIG. 6 in accordance with oneembodiment of the present invention.

FIGS. 12A and 12B are simplified perspective views illustrating the useof an actuation signal in accordance with another embodiment of thepresent invention with a complex dynamic system that is actuated usingelectromagnetic attraction.

FIGS. 13A and 13B are simplified perspective views illustrating the useof an actuation signal in accordance with another embodiment of thepresent invention with a MEMS switching cell that is actuated usingelectromagnetic attraction.

FIG. 14 is a block diagram illustrating an exemplary system forconstructing and supplying the actuation signal to a MEMS array inaccordance with an embodiment of the present invention.

FIG. 15 is a plot illustrating the effects of varying the offset andduration of the divot in the actuation signal of FIG. 6.

FIG. 16 illustrates a method for determining a damping characteristicfor each of the switches in an array in accordance with animplementation of the present invention.

FIG. 17 is a block diagram illustrating an exemplary system forconstructing and supplying the actuation signal to a MEMS array inaccordance with an embodiment of the present invention.

FIG. 18 is a block diagram illustrating an exemplary system forconstructing and supplying the actuation signal to a MEMS array inaccordance with an embodiment of the present invention.

DESCRIPTION

This application hereby incorporates by reference in its entirety, U.S.patent application Ser. No. 09/783,730, by Kruglick, et al., entitledMETHOD AND APPARATUS FOR ELECTRONIC DAMPING OF COMPLEX DYNAMIC SYSTEMS,and hereby incorporates by reference in its entirety U.S. patentapplication Ser. No. 09/896,022, filed herewith, by Kruglick, entitledELECTRONIC DAMPING OF MEMS DEVICES USING A LOOK-UP TABLE.

The following description is not to be taken in a limiting sense, but ismade for the purpose of describing one or more embodiments of theinvention. The scope of the invention should be determined withreference to the claims.

Referring to FIG. 1, there is illustrated an optical crossbar switch100, or simply, an optical switch 100. The optical switch 100 is atwo-dimensional (2D) optical switch that is capable of providingswitchable cross connects between an array of input fibers 103 and anarray of output fibers 121. Specifically, the optical switch 100provides an array of free-space optical connections between the inputand output fibers 103, 121. This enables each of a plurality of opticalinput channels to be directed to a desired optical output channel. Eachof the optical input channels may also be dropped via the droppedchannel fibers 123, or other channels may be added via the add channelfibers 111 to replace certain input channels. That is, the opticalswitch is capable of performing optical switching as well aswavelength-selective add/drop filtering.

A cable 102 containing a plurality of input fibers 103 is incident upona demultiplexer 104, which separates the optical beam carried by eachfiber into a number of input channels. The input channels are provided,via a collimator array 106, to an array 108 of optomechanical switchingcells. Similarly, a cable 110 containing a plurality of add channelfibers 111 is incident upon a demultiplexer 112 followed by a collimatorarray 114. The optomechanical switching cells can be configured todirect particular input channels to desired output channels, as well asto implement the channel add/drop functionality mentioned above.Separate multiplexers 116, 118 are provided for multiplexing the outputchannels and the “dropped” channels onto the fibers 121, 123 of separatecables 120, 122, respectively.

The array 108 of optomechanical switching cells are connected to asubstrate 124. The optomechanical switching cells are preferablyfabricated in accordance with Micro-Electro-Mechanical Systems (MEMS)technology. Each of the switching cells includes a mirror and anactuator. The lenses of the collimator arrays and the mirrors of eachMEMS switching cell are aligned so that each switching cell canselectively intercept a beam output from one of the collimator arrays.

FIGS. 2 and 3 are simplified diagrams illustrating an exemplary MEMSswitching cell 200 that may be included in the array 108 ofoptomechanical switching cells. A micromirror 202 is mounted to anactuator plate 204. The actuator plate 204 is hingedly connected to thesubstrate 124 with a torsion hinge 206, which by way of example may beof the type described in U.S. patent application Ser. No. 09/697,762,filed Oct. 25, 2000, entitled “MEMS Optical Switch with Torsional Hingeand Method of Fabrication Thereof”, by inventor Li Fan, and identifiedby attorney docket number 1008, the entire contents of which are herebyexpressly incorporated by reference into the present application as iffully set forth herein. The micromirror 202 is shown in a verticalposition with the mirror surface being perpendicular to the substrate124. Another torsion hinge (not shown) may be used to permit themicromirror 202 to pivot relative to the actuator plate 204.

FIG. 2 illustrates the switching cell 200 in its transmission state, andFIG. 3 illustrates the switching cell 200 in its reflection state. Inthe reflection state, the actuator plate 204 rests on a motion stop 208(or other landing structure) mounted on the substrate 124. By way ofexample, the motion stop 208 may comprise a jack stop of the typedescribed in U.S. patent application Ser. No. 09/697,767, filed Oct. 25,2000, entitled “MEMS Microstructure Positioner and Method of FabricationThereof”, by inventor Li Fan, and identified by attorney docket number1013, the entire contents of which are hereby expressly incorporated byreference into the present application as if fully set forth herein.During operation, an optical beam 210 is incident at an approximately45° angle from the normal of the micromirror 202. By pivoting theactuator plate 204 about the torsion hinge 206, the micromirror 202 ismoved in and out of the path of the optical beam 210, switching theoutput of the optical beam 210 between a reflection direction 212 andthe transmission direction (210 of FIG. 2).

The actuator plate 204, an actuator electrode 214 mounted on thesubstrate 124, and the gap therebetween form an electrostatic actuator.In one embodiment, the switching cell 200 is activated by a circuit thatselectively develops an electrostatic force between the actuator plate204 and the actuator electrode 214. This force causes the actuator plate204 and the micromirror 202 mounted thereto to pivot in angular positionrelative to the substrate 124, i.e., in the direction indicated by arrow216. In other words, when a voltage bias, symbolized by voltage source218, is applied between the actuator plate 204 and the actuatorelectrode 214 (or substrate 124), the actuator plate 204 is caused todraw close and contact the motion stop 208. Thus, a voltage bias isapplied between the actuator plate 204 and the actuator electrode 214 tocause the switching process by electrostatic attraction. Alternateactuation methods/forces may also be used, such as for example,electromagnetic, thermal expansion, and piezoelectric. Such alternateactuation methods/forces will be discussed below.

Because of the presence of the motion stop 208, the MEMS switching cell200 forms a complex dynamic system for purposes of analyzing the angularmovement of the actuator plate 204. A complex dynamic system may also bereferred to as a nonlinear system. The MEMS switching cell 200 forms acomplex dynamic system because the motion stop 208 causes the actuatorplate 204 to move in a vibrating manner when the actuator plate 204impacts the motion stop 208.

In order to bring the actuator plate 204 to rest on the motion stop 208as quickly as possible, damping is used. The damping of movingstructures in complex dynamic systems is difficult, and such systems donot lend themselves to conventional methods of damping. In order toillustrate this difficulty, reference is made to FIG. 4, whichillustrates a conventional actuation signal 230 and the resulting outputsignal 232 for the MEMS switching cell 200. In accordance with knownprinciples, the actuation signal 230 can be made to provide effectivedamping in many non-complex dynamic systems that do not have motionstops. FIG. 4 illustrates the result of application of the actuationsignal 230 to the switching cell 200, which is a complex dynamic system.

The actuation signal 230 is applied to the electrostatic actuator, i.e.,between the actuator plate 204 and the actuator electrode 214, to createa force that pulls the actuator plate 204 towards the motion stop 208.The resulting output signal 232 represents the optical power of theoutput optical beam 212 that is reflected off of the micromirror 202.

As illustrated, shortly after the actuation signal 230 is activated, theoutput signal 232 starts oscillating and then eventually settles in itson state, i.e., full optical power of the reflected output optical beam212. The output signal 232 oscillates because the downward forceimparted on the actuator plate 204 by the actuation signal 230 causesthe actuator plate 204 to bounce off of the motion stop 208 severaltimes. This bouncing, depicted in FIG. 5, causes the micromirror 202 tomove through and within the optical path several times, which switchesthe output optical beam 212 between the reflection and the transmissionstates several times creating the oscillating output signal 232. In thisexample, it takes 11.36 milliseconds (ms) for the output signal 232 toreach 90% settlement. As evidenced by this rather lengthy settlementtime, the actuation signal 230 does not provide quick and efficientdamping in complex dynamic systems that have motion stops.

It is desirable to minimize the settlement time of the actuator plate204 in order to reduce the switching time. Such a reduction in theswitching time of the MEMS switching cells increases the performance ofthe optical switch 100. The settlement time of the actuator plate 204can be reduced by employing a damping method that provides moreeffective damping than the damping provided by the actuation signal 230.

Referring to FIG. 6, there is illustrated an actuation signal 240 inaccordance with one embodiment of the present invention. The actuationsignal 240 provides highly effective damping of a structure in a complexdynamic system having a positive motion stop. Similar to above, theactuation signal 240 is the signal that is applied between the actuatorplate 204 and the actuator electrode 214 to create a force that pullsthe actuator plate 204 towards the motion stop 208. The resulting outputsignal 242 represents the optical power of the output optical beam 212that is reflected off of the micromirror 202.

As illustrated, shortly after the actuation signal 240 is activated, theoutput signal 242 rises above 90% of its maximum level and stays there.The oscillations in the output signal 242 are small and do not fallbelow the 90% level. In this example, it takes only 3.5 ms for theoutput signal 242 to reach 90% settlement. Thus, the actuation signal240 provides a greatly reduced settling time as compared to the settlingtime achieved with the actuation signal 230 of FIG. 4.

The actuation signal 240 provides highly effective damping because itreduces the magnitude of bouncing off of the motion stop 208 and reducesthe length of time that the actuator plate 204 bounces off of the motionstop 208. These features reduce the settling time of the actuator plate204. In this way, the actuation signal 240 provides electronic dampingof the actuator plate 204.

Referring to FIG. 7, the actuation signal waveform 240 provides highlyeffective and simple to implement electronic damping for the actuatorplate 204 (of FIGS. 2 and 3) at the mechanical motion stop 208 (of FIGS.2 and 3). Important characteristics of the signal 240 are a decrease indrive timed with respect to the first impact of the moving actuatorplate 204 on the motion stop 208. Specifically, the actuation signalwaveform 240 preferably begins with an acceleration phase 244 duringwhich the actuator plate 204 accelerates towards the motion stop 208. Inone embodiment, the acceleration phase 244 involves the application of asubstantially constant magnitude voltage between the actuator plate 204and the actuator electrode 214 (of FIGS. 2 and 3). The accelerationphase 244 is followed by a coast phase 246 where the acceleration of theactuator plate 204 is decreased as it approaches the motion stop 208.The coast phase 246 involves decreasing the magnitude of the actuationvoltage in a linear manner prior to the actuator plate 204 impacting themotion stop 208. Next, a segue phase 248 increases the downward force onthe actuator plate 204 at about the time the actuator plate 204 impactsthe motion stop 208. The segue phase 248 involves increasing themagnitude of the actuation voltage in a linear manner. Finally, a holddown phase 250 applies maximum downward force to the actuator plate 204to hold it against the motion stop 208. The hold down phase 250 involvesleveling off the magnitude of the actuation voltage.

FIG. 8A illustrates the torque and velocity of the actuator plate 204(of FIGS. 2 and 3) resulting from the actuation signal 230 (of FIG. 4),and FIG. 8B illustrates the torque and velocity of the actuator plate204 resulting from the actuation signal 240 (of FIG. 6). Torque and theactuation signal voltage have the following approximate electrostaticrelationship: $\begin{matrix}{{Torque} \propto \frac{{Voltage}^{2}}{{gap}^{2}}} & (1)\end{matrix}$

where the “gap” is the distance between the actuator plate 204 and theactuator electrode 214.

With the actuation signal 230, the torque and velocity continue toincrease right up to the motion stop 208. This causes severe bouncing ofthe actuator plate 204. In contrast, with the actuation signal 240, thetorque and velocity do not continue to increase right up to the motionstop 208. Instead, the torque and velocity decrease somewhat from thevalues which signal 230 would cause before reaching the motion stop 208,which reduces the strength of the bounce of the actuator plate 204.

Referring to FIG. 7, important parameters for the actuation signalwaveform 240 are: (1) the total time “η” for the acceleration and coastphases 244, 246; and (2) the decrease (or depth) in voltage “d” duringthe coast phase 246. In one embodiment of the invention, the depth ofmodulation “d” is chosen to target an approximately 30-50% reduction indrive as the actuator plate 204 touches down on the motion stop 208. Byway of example, “d” may be approximately equal to 40-60% of thesubstantially constant magnitude of the acceleration phase 244.Furthermore, by way of example, the coast phase 246 may involvedecreasing the magnitude of the actuation signal from the substantiallyconstant magnitude of the acceleration phase 244 by the value “d” in anamount of time “τ”, where “τ” falls in the range of 1 to 3 ms for theillustrated embodiment.

The value of “η” is preferably chosen to approximately target the firstpeak in the output signal 232 in FIG. 4, thus lowering the drive just astouchdown occurs. This way the “divot” formed by the coast and seguephases 246, 248 hits just as the actuator plate 204 (of FIGS. 2 and 3)touches down upon the motion stop 208 (of FIGS. 2 and 3), whichminimizes the force at approximately the time of contact. Thus, theacceleration and coast phases 244, 246 comprise a total amount of timeapproximately equal to the time it takes the undamped actuator plate 204to reach the motion stop 208.

Thus, the actuation signal waveform 240 is typically tuned in amplitudeor frequency. Namely, the amplitude sets “d” and thus the magnitude ofthe acceleration and hold down phases 244, 250, and the frequency sets“η” and thus the coast and segue phases 246, 248.

It was mentioned above that the coast and segue phases 246, 248preferably involve decreasing and increasing, respectively, themagnitude of the actuation signal in a linear manner. It should be wellunderstood, however, that such linear decreasing and increasing is not arequirement of the present invention. Namely, either or both of thecoast and segue phases 246, 248 may alternatively be implemented bydecreasing and increasing, respectively, the actuation signal in anonlinear manner in accordance with the present invention. For example,FIG. 9A illustrates a linear coast phase 262 and a nonlinear segue phase264, and FIG. 9B illustrates a nonlinear coast phase 270 and a linearsegue phase 272. Although the linear scheme provides for ease ofimplementation, a nonlinear scheme may be employed by the presentinvention.

In addition, the acceleration and hold down phases 244, 250 are notrequired to have the same magnitude. For example, FIG. 9C illustratesthe acceleration phase 278 having a greater magnitude than the hold downphase 280, and FIG. 9D illustrates the acceleration phase 286 having asmaller magnitude than the hold down phase 288. Nonlinear coast andsegue phases 290, 292 are also shown.

FIG. 9E illustrates that one or more additional fluctuations 294 may beinserted into the actuation signal between the segue phase 296 and thehold down phase 298 in accordance with the present invention.

FIG. 9F illustrates that the coast and segue phases 261, 263 may also beimplemented as a negative pulse in accordance with the presentinvention. Namely, the decreased voltage of the coast and segue phases261, 263 form a pulse, providing in essence a pulsewidth modulatedoutput signal.

Referring to FIG. 10, there is illustrated an actuation signal 275 inaccordance with another embodiment of the present invention. Theactuation signal 275 also provides highly effective damping of astructure in a complex dynamic system having a positive motion stop.Similar to above, the actuation signal 275 is applied between theactuator plate 204 (of FIGS. 2 and 3) and the actuator electrode 214 (ofFIGS. 2 and 3) to create a force that pulls the actuator plate 204towards the motion stop 208 (of FIGS. 2 and 3). The resulting outputsignal 277 represents the optical power of the output optical beam 212(of FIG. 3) that is reflected off of the micromirror 202 (of FIG. 3).

The actuation signal 275 includes only two phases, namely, anacceleration phase 279 and a hold down phase 281. Because there are onlytwo phases, the actuation signal 275 may be referred to as a “two-step”actuation signal. In the illustrated embodiment, the acceleration phase279 involves the application of a substantially constant magnitudevoltage between the actuator plate 204 and the actuator electrode 214.Following the acceleration phase 279 is the hold down phase 281, whichinvolves the application of a substantially constant magnitude voltagebetween the actuator plate 204 and the actuator electrode 214 that issmaller than the magnitude applied during the acceleration phase 279.

As illustrated, shortly after the beginning of the acceleration phase279, the output signal 277 starts a wide oscillation. This wideoscillation is a result of the actuator plate 204 accelerating towardthe motion stop 208 and then bouncing off of it with fairly largemagnitude bounces. The hold down phase 281 causes the magnitude of thebounces to decrease and the output signal 277 to eventually settle inits on state, i.e., full optical power of the reflected output opticalbeam 212. In this example, the acceleration phase 279 continues for 3ms, and the magnitude of the hold down phase 281 is equal to 40% of themagnitude of the acceleration phase 279. With these values it takes 8.1ms for the output signal 277 to reach 90% settlement. Thus, theactuation signal 275 provides a reduced settling time as compared to thesettling time achieved with the actuation signal 230 of FIG. 4.Referring to FIG. 11, there is illustrated an exemplary high voltagesystem 300 for generating the actuation signal waveform 240 inaccordance with one embodiment of the present invention. An inputvoltage is received at V_(input). The input voltage is typically aconventional digital signal falling in the range of 0-5 Volts. Theactuation signal waveform 240 is output at V₂₄₀.

A microprocessor 302 monitors V_(input). When V_(input) goes high, themicroprocessor 302 controls a high voltage source 304 to produce a highvoltage at output V₂₄₀. Furthermore, the microprocessor 302 controls thehigh voltage source 304 to produce the acceleration, coast and seguephases 244, 246, 248 in the output of the high voltage source 304. The“divot” formed by the coast and segue phases 246, 248 is included in thehigh voltage signal produced at V₂₄₀. The high voltage source 304 can bebased on a standard drive voltage that, by way of example, may be equalto the magnitude of the hold down phase 250 of the actuation signal 240.

The above discussion focused on the use of electrostatic attraction tocause the switching process in the switching cell 200 (of FIGS. 2 and3). Namely, the actuation signal 240 (of FIG. 6) is illustrated as avoltage in the figures. It should be well understood, however, that theactuation signals described herein, i.e., the actuation signal 240 andthe actuations signals illustrated in FIGS. 9A, 9B, 9C, 9D, 9E, 9F and10, may be used with many different types of actuation methods/forces inaccordance with the present invention. For example, the actuationsignals described herein may be used with electromagnetic attraction,thermal expansion, or piezoelectric attraction. When used with thesealternate actuation methods/forces, the actuation signals describedherein provide highly effective damping of structures in complex dynamicsystems.

FIGS. 12A and 12B illustrate the manner in which the actuation signalsof the present invention can be used to provide highly effective dampingin a complex dynamic system 400 that is actuated using electromagneticattraction. Specifically, the complex dynamic system 400 includes amovable structure 402 that is connected to a hinge 404. The movablestructure 402 comprises a ferrous or paramagnetic material and isstopped by a motion stop 406. An actuation signal 408 in accordance withthe present invention is applied to an electromagnet 410. In thisembodiment, the actuation signal 408 is a current I₄₀₈ that causes theelectromagnet 410 to create a force that pulls the moveable structure402 towards the motion stop 406. The actuation signal 408, which mayhave the waveform shape of any of the actuation signals described above,provides highly effective damping for the same reasons discussed above.Namely, the actuation signal 408 provides a decrease in drive timed withrespect to the first impact of the moveable structure 408 on the motionstop 406.

FIGS. 13A and 13B illustrate a MEMS switching cell 430 that is actuatedusing electromagnetic attraction. A micromirror 432 is mounted to anactuator plate 434. The actuator plate 434 comprises a ferrous orparamagnetic material and is hingedly connected to the substrate 436with a torsion hinge 438. FIG. 13A illustrates the switching cell 430 inits transmission state where the optical beam 440 is not reflected. FIG.13B illustrates the switching cell 430 in its reflection state where theoptical beam 440 is switched to a reflection direction 442. In thereflection state, the actuator plate 434 rests on a motion stop 444 (orother landing structure) mounted on the substrate 436.

The actuator plate 434, an electromagnet 446 mounted on the substrate436, and the gap therebetween form an electromagnetic actuator. Theswitching cell 430 is activated by providing an actuation signal 448 tothe electromagnet 446. In this embodiment, the actuation signal 448 is acurrent I₄₄₈. The current I₄₄₈ causes the electromagnet 446 to create aforce that causes the actuator plate 434 and the micromirror 432 mountedthereto to pivot in angular position relative to the substrate 436,i.e., in the direction indicated by arrow 450. This force causes theactuator plate 434 to draw close and contact the motion stop 444. Thus,by applying the actuation signal 448 to the electromagnet 446, theswitching process is effectuated by electromagnetic attraction.

In accordance with the present invention, the actuation signal 448 maycomprise the waveform shape of any of the actuation signals describedabove, i.e., the actuation signal 240 and the actuation signalsillustrated in FIGS. 9A, 9B, 9C, 9D, 9E, 9F and 10. The use of suchwaveform shapes for the current I₄₄₈ provides highly effective dampingof the actuator plate 434. Highly effective damping is achieved becausethe current I₄₄₈ provides a decrease in drive timed with respect to thefirst impact of the actuator plate 434 on the motion stop 444.

The entire contents of U.S. patent application Ser. No. 09/063,644,filed Apr. 20, 1998, entitled “Micromachined Optomechanical Switches”,and U.S. patent application Ser. No. 09/483,276, filed Jan. 13, 2000,entitled “Micromachined Optomechanical Switching Cell with ParallelPlate Actuator and On-Chip Power Monitoring”, are hereby expresslyincorporated by reference into the present application as if fully setforth herein.

Turning to FIG. 14, as discovered by the present inventors, controllingsystem damping can be further complicated in a MEMS array 500. This isbecause each of the switches 500 a ₀, 500 a ₁, 500 a ₂, etc., in thearray 500 can have different damping characteristics. This may be due todevice non-uniformities, which can result from the fabrication process.For example, switches near the periphery of the array may have differentdamping characteristics than switches near a central portion of thearray. Such a situation further adds to the complexity of providingeffective damping for the system.

Shown in FIG. 14, a single high voltage source 504 may be utilized toprovide actuation signals to all of the switches 500 a ₀, 500 a ₁, 500 a₂, etc., in the array 500. In such a system, a single actuation signalcan be selected to take into account damping non-uniformities occurringin the switch array 500.

To determine a single actuation signal for operating the array, anactuation signal having a decreased drive portion is selected asdiscussed above with reference to FIGS. 6, 7, and 9A-9F. In theimplementation of FIG. 14, during operation of the switch array 500, thehigh voltage source 504 is applied not only to a selected switch forswitching, as well as to any and all switches already energized. Thus,in this example, the actuation signal should be selected so as toinhibit already energized switches from moving, or otherwise changingtheir switch state. Hence, in the MEMS optical switch example discussedabove with reference to FIG. 5, the depth of modulation “d” is chosen toreduce the drive of the actuator plate or actuator arm 204, but not toallow release of any energized switches in the array 500.

Turning to FIG. 15, the selected actuation signal 240 is applied to eachof the switches of the array 500 to determine a range of values of adamping coefficient z for each switch that provide settling times inconformance with a predetermined specification. The damping coefficientz sets the time η (shown in FIG. 7). In addition, the dampingcoefficient z is used to define the relationship between an offset ofthe coast phase 246 with respect to beginning of the acceleration phase244, and the combined duration of the coast and seque phases 246 and 248(both shown in FIG. 7). Thus, the damping coefficient z can be utilizedto proportionally vary the offset and the combined duration asillustrated in FIG. 15. Increasing the damping coefficient z decreasesthe time η (shown in FIG. 7). FIG. 15 depicts how the dampingcoefficient z can be used to proportionally change the offset andduration of the coast and seque phases (shown as divots 247 a-h) of theselected actuation signal 240 of FIG. 7. In FIG. 15, multiple divots 247a-h are shown in the selected actuation signal 240 in response tomultiple selected damping coefficients z. Thus, In this way, a range ofvalues for the damping coefficients z of the selected waveform can beexpediently determined for each of the switches in the array 500.

Turning to FIG. 16, in one implementation for example, an initial valuefor the damping coefficient z_(i) can be determined by using a teststation to scan for an initial value of the damping coefficient z_(i)that provides a settling time in conformance with a predeterminedspecification as illustrated at box 1610. The damping coefficient z maythen be successively increased from its initial value z_(i) to determinea maximum value of the damping coefficient z_(max) that produces asettling time in conformance with the predetermined specification,illustrated in boxes 1620 and 1630. The maximum damping coefficientz_(man) is then recorded 1640. The minimum value of the dampingcoefficient z_(min) is determined, such as by returning to the initialdamping coefficient z_(i) and successively decreasing the dampingcoefficient z to ascertain settling times in conformance with thepredetermined specification, illustrated by boxes 1650, 1660, and 1670.The minimum damping coefficient z_(min) is recorded 1680.

Typically, this is carried out at an ambient pressure similar to thedevice operating conditions. As such, it can be carried out afterhermetically sealing of the package containing the MEMS chip.

Referring to FIG. 14, the ranges of values that produce settling timesin conformance with the predetermined specification for each of theswitches in the array 500 are used to select an operating dampingcoefficient z_(oper) to be utilized by the microprocessor 502 to controlthe high voltage source 504. In one implementation, the operatingdamping coefficient z_(oper) is selected midway between, the largestvalue of the minimum damping coefficient z_(min) for all the switches inthe array, and the smallest value of the maximum damping coefficientz_(max) for all the switches in the array 500.

The microprocessor 502 is programmed to construct a single operatingactuation signal having the values of the offset and combined durationcorresponding to the operating damping coefficient z_(oper). Toconstruct the operating actuation signal, the microprocessor 502monitors for commencement of an actuation signal to a switch, such as bymonitoring the incoming digital user input supplied to the selector 506.After commencement of an actuation signal has been detected by themicroprocessor 502, the microprocessor controls the high voltage signalsource 504 to provide a divot, or other selected signal reduction at itsoutput. As discussed above, in the implementation of FIG. 14, the divotor other selected signal reduction is supplied not only to the structurebeing moved but also to any switches currently energized or otherwisereceiving a signal from the high voltage source 504.

It is also possible to construct a custom operating actuation signal foreach switch using the determined settling characteristics for eachswitch. This may be accomplished by using the stored values of theminimum and maximum damping coefficients z_(min) and z_(max) for eachswitch. Or, a custom damping coefficient z_(cust) that provides the bestmeasured settling time for each switch could be stored and utilized bythe microprocessor 502 to construct a custom operating actuation signalfor each switch. The custom values may be stored in a look-up tableformat that is accessed by the microprocessor 602 for selecting thecorresponding stored custom damping coefficient for each switch. Anindividual damping coefficient could be stored in the look-up table withreference to the switch's position in the array, i.e. by column and row.The custom values in the look-up table, which can be the correspondingoffset and combined duration, can be utilized to construct a customoperating actuation signal for each switch.

Turning to FIG. 17, it is also possible to employ several high voltagesources 604 a-d to provide actuation signals to the switches of thearray 600. In the implementation of FIG. 17, one high voltage source 604a provides actuation signals for a column 600 a of switches 600 a ₀-a₃.This allows switches in the different columns 600 a-d to be switchedcontemporaneously and/or near contemporaneously without having to waitfor a single shared high voltage source 502 to return to an accelerationphase voltage. For example, a switch may be actuated before the divot246, 248, shown in FIG. 7, which is being applied to a switch in anothercolumn has finished.

Further, because obtaining values from a large look-up table can bemicroprocessor intensive, utilizing several microprocessors 604 a-dallows for smaller look-up tables be used in implementing the customoperating actuation signals. For example, one look-up table associatedwith processor 602 a stores the values for the switches in column 600 a,and another look-up table associated with processor 602 b stores thevalues for the switches in column 600 b, and so on. This can reducecosts by allowing slower less expensive microprocessors to be used.Multiple processors also facilitates contemporaneous and/or nearcontemporaneous switching of switches in the different columns.

It is possible to provide separate microprocessor controlled highvoltage sources for each of the switches in the array 600. In aconventional optical cross-connect, however, no more that one switch ina column is switched at a time. Thus, for the 4×4 array 600, four highvoltage sources are sufficient. Further, as array sizes grow to 8×8,16×16, and beyond, providing a microprocessor, a DAC, and a high voltagesupply for each column ultimately will be more practical than providinga microprocessor, a DAC, and a high voltage supply for each switch.

Turning to FIG. 18, a single microprocessor 602 may be utilized toconstruct custom operating actuation signals using multiple high voltagesources 604 a-d. As discussed above, a single microprocessor requires alarger look-up table, and therefore typically would require a higherperformance microprocessor than with the multiple processorimplementation of FIG. 17.

Referring to FIGS. 14, 17 and 18, although shown as a single block, theselector 506, 606 may be a single component, or it may comprise, orequivalently be, several individual selectors. Thus, a selector 506 or606 may be a selector that is a single or multiple component device.

Constructing a custom actuation signal for each switch allows bettersettling time for the switches in the array. The custom actuation signalhas been discovered by the present inventors to provide about 50% bettersettling times.

Although in some implementations discussed above the offset of the coastphase with respect to the commencement of the acceleration phase and thecombined duration of the coast phase and the seque phase can be variedproportionally, it is also possible to independently vary the offsetand/or the combined duration. Further, it is possible to vary one of thewaveforms controlling parameters, such as the offset, the combinedduration, or the independent durations of the coast or seque phaseswhile an other is held constant.

While the invention herein disclosed has been described by the specificembodiments and applications thereof, numerous modifications andvariations could be made thereto by those skilled in the art withoutdeparting from the scope of the invention set forth in the claims.

What is claimed is:
 1. A method for operating a plurality of MEMSdevices comprising: a) applying a magnitude of a selected actuationsignal equal to a first substantially constant magnitude to an actuatorto cause a movable structure to begin to accelerate from a firstposition to impact a motion stop at a second position; b) decreasing themagnitude of the selected actuation signal in a first manner; c) varyingat least one of a start time and a duration of the decreasing magnitudeof the selected actuation signal; d) observing a settling time of themovable structure in response to the step of varying; e) ascertaining arange of values for the start times and the corresponding durations foreach of the plurality of MEMS devices capable of providing settlingtimes of the movable structure in conformance with a predeterminedspecification based on the steps of varying and observing; f) using theascertained range of values for each of the plurality of MEMS devicesand the selected actuation signal, determining an operating start timeand a corresponding operating duration to construct an operatingactuation signal capable of providing a settling time for each of theplurality of MEMS devices in conformance with the predeterminedspecification; and g) controlling a signal source with a programmedprocessor to selectively apply the operating actuation signal to theplurality of MEMS devices.
 2. The method of claim 1 wherein controllingthe signal source further comprises applying the signal source outputsignal to all of the plurality of MEMS devices receiving an actuationsignal.
 3. The method of claim 1 wherein controlling the signal sourcewith the processor comprises decreasing a magnitude of an output of thesignal source using the operating start time and the correspondingoperating duration.
 4. The method of claim 3 wherein controlling thesignal source comprises generating a divot in the output of the signalsource.
 5. The method of claim 1 wherein controlling the signal sourcewith the preprogrammed processor comprises applying the decreasingmagnitude portion with the determined operating start time andcorresponding operating duration to all of the plurality of MEMS devicesenergized by the processor.
 6. The method of claim 1 wherein observingcomprises storing values of start times and corresponding durations inconformance with the predetermined specification.
 7. The method of claim6 wherein determining comprises: a) determining a start timesubstantially representing an average between: a maximum start time forthe plurality of MEMS devices producing a value of the settling time ofthe movable structure in conformance with a predetermined specification,and a minimum start time for the plurality of MEMS devices producing avalue of the settling time of the movable structure in conformance withthe predetermined specification; and b) determining a correspondingduration substantially representing an average between: a maximumcorresponding duration for the plurality of MEMS devices producing avalue of the settling time of the movable structure in conformance witha predetermined specification, and a minimum corresponding duration forthe plurality of MEMS devices producing a value of the settling time ofthe movable structure in conformance with the predeterminedspecification.
 8. The method of claim 1 wherein decreasing the magnitudeof the actuation signal in a first manner comprises decreasing themagnitude of the actuation signal in a linear manner.
 9. The method ofclaim 1 further comprising increasing the magnitude of the operatingactuation signal in a second manner subsequent to decreasing themagnitude.
 10. The method of claim 9 further comprising leveling off themagnitude of the operating actuation signal at a second substantiallyconstant magnitude subsequent to increasing the magnitude.
 11. Themethod of claim 9 further comprising leveling off the magnitude of theoperating actuation signal at the first substantially constant magnitudesubsequent to increasing the magnitude.
 12. The method of claim 9wherein increasing the magnitude of the actuation signal in a secondmanner comprises increasing the magnitude of the actuation signal in alinear manner.
 13. The method of claim 12 wherein decreasing themagnitude of the actuation signal in a first manner comprises decreasingthe magnitude of the actuation signal in a linear manner.
 14. The methodof claim 9 comprising at least one of: (a) decreasing the magnitude ofthe actuation signal in a non-linear manner, or (b) increasing themagnitude of the actuation signal in a nonlinear manner.
 15. The methodof claim 1 further comprising applying an actuation voltage between anactuator arm pivotally coupled to a substrate and an electrode locatedbelow the second position and adjacent the substrate.
 16. The method ofclaim 1 further comprising actuating a mirror structure transverselymounted to the actuator arm to switch optical signal.
 17. A method fordetermining and implementing electrical damping coefficients for aplurality of MEMS devices, the method comprising: a) constructing andsupplying a plurality of actuation signals to each of the plurality ofMEMS devices; b) wherein constructing and supplying comprises causing amovable structure to begin to accelerate from a first position towards asecond position and to impact a motion stop; c) wherein constructing andsupplying each of the plurality of actuation signals comprises: (i)providing the actuation signal with a first portion of a substantiallyconstant magnitude; (ii) providing the actuation signal with a portiondecreasing to a second magnitude following the first portion; (iii)providing the actuation signal with a portion increasing from the secondmagnitude subsequent to decreasing to the second magnitude; (iv)providing the second magnitude offset from a commencement of the firstportion; (v) providing the decreasing portion and the increasing portionwith a combined duration; and (vi) ascertaining a range of values forthe offset of the second magnitude and the corresponding combinedduration for each of the plurality of MEMS devices that provide settlingtimes of the movable structure in conformance with the predeterminedspecification; and d) programming a processor to construct a singleoperating actuation signal for the plurality of MEMS devices capable ofcausing the movable structure to begin to accelerate from the firstposition towards the second position and to impact the motion stop so asto provide settling times for the movable structure for each of theplurality of MEMS devices in conformance with the predeterminedspecification using the ascertained range of values for each of theplurality of MEMS devices.
 18. The method of claim 17 whereinascertaining comprises varying the second magnitude offset and thecombined duration proportionally.
 19. The method of claim 18 comprisingprogramming the processor control a signal source so as to substantiallyprovide the first substantially constant magnitude portion, thedecreasing portion, and the increasing portion at an output of thesignal source.
 20. The method of claim 19 comprising programming theprocessor to control the signal source so as to generate a divot in theoutput of the signal source.
 21. The method of claim 20 whereinconstructing and supplying comprises providing the actuation signal witha second portion of the substantially constant magnitude after providingthe increasing portion.
 22. The method of claim 21 wherein providing theactuation signal with the decreasing portion comprises providing alinearly decreasing portion, and wherein providing the actuation signalwith the increasing portion comprises providing a linearly increasingportion.
 23. The method of claim 17 comprising programming the processorcontrol a signal source so as to substantially provide the firstsubstantially constant magnitude portion, the decreasing portion, andthe increasing portion at an output of the signal source.
 24. The methodof claim 17 comprising providing the second magnitude offset and thecombined duration with substantially a same duration.
 25. The method ofclaim 24 wherein ascertaining comprises varying the second magnitudeoffset and the combined duration simultaneously.
 26. The method of claim17 comprising: a) wherein constructing and supplying comprises providingthe actuation signal with a second portion of the substantially constantmagnitude after providing the increasing portion; b) wherein providingthe actuation signal with decreasing portion comprises providing alinearly decreasing portion; and c) wherein providing the actuationsignal with increasing portion comprises providing a linearly increasingportion.
 27. The method of claim 17 wherein ascertaining the range ofvalues for each of the plurality of MEMS devices comprises: a) selectinginitial values for the offset of the second magnitude and for acorresponding combined duration to provide a settling time inconformance with a predetermined specification; b) increasing the offsetof the second magnitude and the corresponding combined duration from theinitial values; and c) decreasing the offset of the second magnitude andthe corresponding combined duration from the initial values.
 28. Themethod of claim 27 wherein ascertaining the range of values for each ofthe plurality of MEMS devices comprises: a) determining maximum valuesfor the offset of the second magnitude and the corresponding combinedduration in conformance with the predetermined specification for each ofthe plurality of MEMS devices; and b) determining minimum values for theoffset of the second magnitude and the corresponding combined durationin conformance with the predetermined specification for each of theplurality of MEMS devices.
 29. The method of claim 28 whereinascertaining the range of values for each of the plurality of MEMSdevices comprises: a) selecting a minimum value of the maximumdetermined values for the offset of the second magnitude and thecorresponding combined duration in conformance with the predeterminedspecification for each of the plurality of MEMS devices; b) selecting amaximum value of the minimum determined values for the offset of thesecond magnitude and the corresponding combined duration in conformancewith the predetermined specification for each of the plurality of MEMSdevices; and c) selecting an operating offset value and correspondingoperating duration for the operating actuation signal between theselected minimum and maximum values.
 30. The method of claim 29 whereinselecting an operating offset value and corresponding operating durationfor the operating actuation signal midway between the selected minimumand maximum values.
 31. The method of claim 17 wherein programmingcomprises programming the processor to control the signal source togenerate a divot in the output of the signal source.
 32. A method foroperating a plurality of MEMS devices comprising: a) generating anactuation signal for actuating a first structure; b) actuating the firststructure to impact a second structure using the actuation signal; c)wherein generating the actuation signal comprises providing a drivephase and a coast phase; d) adjusting at least one of a start time and aduration of the coast phase; e) determining a range of values for eachof the plurality of MEMS switches of the start times and correspondingdurations that provide settling times of the first structure inconformance with a predetermined specification; f) selecting anoperating start time and a corresponding operating duration of the coastphase using the range of values; and g) programming a processor tooperate the plurality of MEMS switches using an operating actuationsignal comprising the selected operating start time and correspondingoperating duration for the coast phase.
 33. The method of claim 32wherein selecting an operating start time and corresponding operatingduration of the coast phase using the range of values for the pluralityof MEMS devices further comprises: a) determining a start time and acorresponding operating duration representing a minimum settling timewithin the range of values; b) determining a start time and acorresponding operating duration representing a maximum settling timewithin the range of values; and c) selecting the operating start timeand an operating duration of the coast phase for the plurality ofswitches using the maximum and minimum settling time values.
 34. Themethod of claim 32 wherein the coast phase is provided prior to impactbetween the first and second structures.
 35. The method of claim 34wherein the coast phase is provided prior to a first impact between thefirst and second structures.
 36. The method of claim 32 whereindetermining whether a settling time of the selected MEMS device conformsto a predetermined specification comprises measuring an optical signalassociated with a selected switch.
 37. The method of claim 32 whereinadjusting at least one of a start time and a duration of the coast phasecomprises simultaneously varying the start time and the duration of thecoast phase.
 38. The method of claim 32 wherein determining a range ofvalues for each of the plurality of MEMS devices comprises: (i)measuring optical signals reflected by each of the plurality of MEMSdevices in response to a plurality of the generated actuation signals;(ii) storing the minimum and maximum values of time to switch theoptical signal within a predetermined criteria so as to determine thesettling time for each of the plurality of switches; (iii) selecting amaximum settling time value from the stored minimum values of time; (iv)selecting a minimum settling time value from the stored maximum valuesof time; and (v) selecting the operating start time and thecorresponding operating duration of the coast phase for the plurality ofswitches using the maximum and minimum settling time values.
 39. Themethod of claim 38 further comprising proportionally varying the starttime and the corresponding duration of the coast phase.
 40. A method fordetermining and implementing electrical damping coefficients for aplurality of MEMS optical switches, the method comprising: a) selectingan actuation signal for causing an actuator arm having a mirror mountedthereon to pivot from a first position towards a second position toimpact a motion stop comprising: (i) providing an acceleration phase ata first substantially constant magnitude; (ii) providing a coast phasedecreasing from the first magnitude to a second magnitude; (iii)providing a segue phase increasing in magnitude following the coastphase; (iv) wherein the actuation signal is constructed such that thesecond magnitude has an offset from a start of the acceleration phase;and (v) wherein the actuation signal is constructed such that the coastphase and the segue phase have a combined duration; b) generating andsupplying a plurality of the selected actuation signal to each of theplurality of MEMS switches; c) ascertaining a range of values of theoffset and the duration of the selected actuation signal for each of theplurality of MEMS devices that provides a settling time of the movablestructure with respect to the motion stop that are in conformance with apredetermined specification, wherein ascertaining comprises: (i)adjusting a frequency associated with the selected actuation signal soas to proportionally adjust the offset and the combined duration; (ii)scanning to determine an initial value of a frequency of the selectedactuation signal that produces a settling time in conformance with thepredetermined specification; (iii) increasing the frequency to ascertaina maximum frequency that produces a settling time in conformance withthe predetermined specification; and (iv) decreasing the frequency toascertain a minimum frequency that produces a settling time inconformance with the predetermined specification; d) selecting a singlefrequency from the range of values for each of the MEMS switches thatprovides settling times for each of the plurality of MEMS switches inconformance with the predetermined specification using the ascertainedrange of values for each of the plurality of MEMS switches; and e)programming a processor to operate the plurality of MEMS switches withthe selected actuation signal at the selected single frequency.
 41. Themethod of claim 40 wherein programming the processor comprisesprogramming the processor to control a signal source to provide theselected actuation signal at the selected single frequency to allenergized switches of the plurality of MEMS switches.
 42. The method ofclaim 41 wherein ascertaining the range of values further comprisesdetecting an optical signal reflected from the mirror to ascertainwhether the adjusted frequency produces a settling time in conformancewith the predetermined specification.
 43. The method of claim 42 whereinproviding the segue phase comprises increasing from the second magnitudeto the first magnitude.
 44. The method of claim 43 wherein providing thecoast phase comprises linearly decreasing from the first magnitude, andwherein providing the segue phase comprises linearly increasing from thesecond magnitude.
 45. The method of claim 44 wherein selecting a singlefrequency comprises selecting a frequency midway between a largest valueof the minimum ascertained frequencies for the plurality of MEMSswitches and a smallest value of the maximum ascertained frequencies forthe plurality of MEMS switches.
 46. A method for determining andimplementing electrical damping coefficients for a plurality of MEMSdevices, the method comprising: a) selecting an actuation signalcomprising a portion for damping an impact between a first and a secondMEMS structure; b) applying the actuation signal to each of theplurality of MEMS devices comprising: (i) applying the selected signalto actuate the first structure to impact the second structure; (ii)varying a damping coefficient of the selected signal; and (iii)observing a settling time of the first structure in response to varieddamping coefficients; c) selecting a damping coefficient based on thestep of observing settling times of each of the plurality of MEMSdevices; d) programming a processor to control an operating actuationsignal for actuating the first structure during operation of theplurality of MEMS devices; and e) wherein programming comprisesprogramming the processor such that the operating actuation signalcomprises the selected actuation signal having the selected dampingcoefficient.
 47. The method of claim 46 wherein programming comprisesprogramming the processor to reduce an output of a signal source aftercommencement of actuation of the first structure to impact the secondstructure.
 48. The method of claim 46 wherein programming comprisesprogramming the processor to construct a single operating actuationsignal for the plurality of MEMS devices.
 49. The method of claim 48wherein observing comprises: a) determining a minimum dampingcoefficient to provide a settling time of the first structure inconformance with a predetermined specification; and b) determining amaximum damping coefficient to provide a settling time of the firststructure in conformance with a predetermined specification.
 50. Themethod of claim 49 wherein selecting a damping coefficient comprisesselecting a damping coefficient midway between a largest minimum dampingcoefficient for the plurality of devices and a smallest maximum dampingcoefficient for the plurality of devices.
 51. The method of claim 46wherein selecting the actuation signal comprises selecting an actuationsignal comprising a divot.
 52. A plurality of MEMS switching devicescomprising: a) a signal source coupled to the plurality of MEMSswitching devices; b) a processor adapted to control the signal sourceso as to provide an actuation signal for actuating impacting structuresof a MEMS switch; c) the processor being configured so as to be capableof providing an actuation signal comprising a drive phase and a coastphase; and d) wherein the processor is configured so as to reducerebounding of the impacting structures.
 53. The apparatus of claim 52further comprising: a) the processor being configured to control thesignal source such that the coast phase has a start time substantiallyrepresenting an average between, a maximum start time for the pluralityof MEMS switching devices producing a value of a settling time of theimpacting structures in conformance with a predetermined specification,and a minimum start time for the plurality of MEMS switching devicesproducing a value of the settling time of the impacting structures inconformance with the predetermined specification; and b) the processorbeing configured to control the signal source such that the coast phasehas a corresponding duration substantially representing an averagebetween, a maximum corresponding duration for the plurality of MEMSswitching devices producing a value of the settling time of theimpacting structures in conformance with a predetermined specification,and a minimum corresponding duration for the plurality of MEMS switchingdevices producing a value of the settling time of the impactingstructures in conformance with the predetermined specification.
 54. Theapparatus of claim 53 wherein the processor is configured to control thesignal source using the start time average and the correspondingduration average such that the coast phase is provided to all theplurality of MEMS switching devices energized by the processor.
 55. Theapparatus of claim 53 wherein the processor is configured to control thesignal source to provide a divot such that the divot comprises the coastphase.
 56. The apparatus of claim 55 wherein the processor is configuredto provide substantially a same magnitude as the drive phase after thedivot.
 57. The apparatus of claim 52 wherein the processor is configuredto control the signal source using the start time average and thecorresponding duration average such that the coast phase is provided toall the plurality of MEMS switching devices energized by the processor.58. The apparatus of claim 52 wherein the processor is configured tocontrol the signal source to provide a divot such that the divotcomprises the coast phase.
 59. The apparatus of claim 58 wherein theprocessor is configured to provide substantially a same magnitude as thedrive phase after the divot.
 60. A MEMS optical switch array comprising:a) a signal source coupled to a plurality of MEMS optical switches; b) ameans for controlling the signal source to provide an actuating signalfor actuating impacting structures of the plurality of MEMS opticalswitches; and c) the means for controlling comprising a means forproviding an actuation signal comprising a drive phase and a coast phaseso as to reduce rebounding of the impacting structure.
 61. The apparatusof claim 60 wherein the means for controlling further comprises: a) ameans for controlling the signal source such that the coast phase has astart time substantially representing an average between, a maximumstart time for the plurality of MEMS switches producing a value of asettling time of the impacting structures in conformance with apredetermined specification, and a minimum start time for the pluralityof MEMS switches producing a value of the settling time of the impactingstructures in conformance with the predetermined specification; and b) ameans for controlling the signal source such that the coast phase has acorresponding duration substantially representing an average between, amaximum corresponding duration for the plurality of MEMS switchesproducing a value of the settling time of the impacting structures inconformance with a predetermined specification, and a minimumcorresponding duration for the plurality of MEMS switches producing avalue of the settling time of the impacting structures in conformancewith the predetermined specification.